Question

What is the nth term of the sequence $1,5,9,13,17$?

• A. $2n-1$
• B. $2n+1$
• C. $4n-3$
• D. none of these

Answer 1

The correct option is C

$4n-3$

Determine $n\mathrm{th}$ term of the sequence $1,5,9,13,17$?

Explanation for correct option:

Option C.

The given sequence is $1,5,9,13,17$.

Find the common difference:

$\begin{array}{rcl}5-1& =& 4\\ 9-5& =& 4\\ 13-9& =& 4\\ 17-13& =& 4\end{array}$

Thus, the common difference is $4$.

Since the common difference is $4$, the given series is an arithmetic progression.

Thus, apply the formula: $a_n=a_1+\left(n-1\right)d$, where $d$ is the common difference and $a_1$ is the first term.

The first term in the given series is $1$, so $a_1=1$.

Substitute $d=4\mathrm{and}{a}_1=1$ into the formula to find the nth term of the given sequence:

$\begin{array}{rcl}{a}_n& =& 1+\left(n-1\right)4\\ a_n& =& 1+4n-4\\ a_n& =& 4n-3\end{array}$

Hence, the correct option is option (C).